The inference of genetic regulatory networks from global measurements of gene expressions is an important problem in computational biology. Recent studies suggest that such dynamical molecular systems are poised at a critical phase transition between an ordered and a disordered phase, affording the ability to balance stability and adaptability while coordinating complex macroscopic behavior. We...

We present a numerical study of a one-dimensional version of the Burridge-Knopoff model [16] of N-site chain of spring-blocks with stick-slip dynamics. Our numerical analysis and computer simulations lead to a set of different results corresponding to different boundary conditions. It is shown that we can convert a chaotic behaviour system to a highly ordered and periodic behaviour by making on...

In this paper we study the so called state maps in the behavioral approach to systems theory. The discussion in this paper continues some preliminary development presented in [5] and it also can be thought of as a generalization of the work in [10]. The concept of states or state variables is present in almost all branches of dynamical systems theory. In areas as remotely connected as discrete ...

We study the network replicator equation and characterize its fixed points on arbitrary graph structures for 2 × symmetric games. show a relationship between asymptotic behavior of existence an independent vertex set in also that complex cannot emerge This links property dynamical system with combinatorial property. contrast this by showing ordinary rock–paper–scissors (RPS) exhibits chaos 3-cy...

Control schemes for dynamical systems typically involve stabilizing unstable periodic orbits. In this paper we introduce a new paradigm of control that involves ‘trapping’ the dynamics arbitrarily close to any desired trajectory. This is achieved by a state-dependent dynamical selection of the input signal applied to the driven nonlinear system. An emergent property of the trapping process is t...

A key condition for the statement of Lasalle’s invariance theorem is the continuity of the trajectories of the dynamical systems with respect to initial conditions. Systems with discontinuous flows generally don’t present such a continuity, but in the particular case of nonsmooth Lagrangian dynamical systems we will see that in fact this continuity property holds in most cases. We will then be ...

The mixing property is characterized by the metric entropy that is introduced by Kolmogorov for dynamical systems. The Kolmogorov entropy is infinite for a stochastic system. In this work a relative metric entropy is considered. The relative metric entropy allows to estimate the level of mixing in noisy dynamical systems. An algorithm for calculating the relative metric entropy is described and...

The global exponential synchronization of complex delayed dynamical networks possessing general topology is investigated in this contribution. The network model considered can represent both the directed and undirected weighted networks. Novel delay-dependent linear controllers are designed via Lyapunov stability theory and appropriate property of the coupling matrix. It is shown that the contr...